Floquet engineering has the advantage of generating new phases with large topological invariants and many edge states by simple driving protocols. In this work, we propose an approach to obtain Floquet topological phases with fourfold-degenerate edge states and even-integer topological invariants in a spin-$1/2$ Creutz ladder model, which is realizable in current experiments. Putting the ladder under periodic quenches, we found rich Floquet topological phases in the system, which belong to the symmetry class $CII$. Each of these phases is characterized by a pair of even integer topological invariants $(w_0,w_{\pi })\in 2\mathbb{Z}\times 2\mathbb{Z}$, which can take arbitrarily large values with the increase of driving parameters. Under the open boundary condition, we further obtain multiple quartets of topological edge states with quasienergies zero and $\pi$ in the system. Their numbers are determined by the bulk topological invariants $(w_0,w_{\pi })$ due to the bulk-edge correspondence. Finally, we propose a way to dynamically probe the Floquet topological phases in our system by measuring a generalized mean chiral displacement. Our findings thus enrich the family of Floquet topological matter, and put forward the detection of their topological properties.

We investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. A barrier initially confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time $t=0$. We investigate the properties of the time-evolved density matrix, the diagonal ensemble density matrix, and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation using exact diagonalization. The weights for the diagonal ensemble and the canonical ensemble match well for high initial temperatures that correspond to negative effective final temperatures after the expansion. At long times after the barrier is removed, the time-evolved Rényi entropy of subsystems bigger than half can equilibrate to the thermal entropy with exponentially small fluctuations. The time-evolved reduced density matrix at long times can be approximated by a thermal density matrix for small subsystems. Few-body observables, like the momentum distribution function, can be approximated by a thermal expectation of the canonical ensemble with strongly suppressed fluctuations. The negative effective temperatures for finite systems go to non-negative temperatures in the thermodynamic limit for bosons, but there is a true thermodynamic effect for fermions, which is confirmed by finite-temperature density matrix renormalization group calculations. We propose the Joule expansion as a way to dynamically create negative temperature states for fermion systems with repulsive interactions.

An optomechanical cavity driven by a periodically amplitude-modulated laser can generate steady light-mechanical entanglement with time periodicity. Similar results can be alternatively obtained by pumping an especially tuned optical degenerate parametric amplifier (DPA) inside the cavity. While the two laser beams are simultaneously applied, the optomechanical entanglement can exhibit constructive and destructive interference patterns, depending on their cooperative phase, which further gives rise to beating in entanglement dynamics if the two modulation frequencies are slightly different, followed by a beating frequency-dependent dynamical behavior in the energy exchange between light and a mechanical oscillator. The optimal dynamical entanglement goes beyond what is attainable by the scenario with two superimposed cavity drivings, as a result of the specially DPA-modulated quantum dynamics. Moreover, we calculate correlation spectra between the cavity and mechanical modes, and we find correspondence between the light-oscillator entanglement and the correlation spectra under the cooperative effect. The cooperation-enhanced optomechanical entanglement is robust against the thermal temperature, and is potentially useful for continuous variable quantum information processing.

A reverse energy flow is theoretically demonstrated to occur in the interference pattern generated by four plane waves with linear polarization. In some regions of the interference pattern, the right-handed triplets of plane-wave vectors k $(k_z>0)$, E, and H (comprising a wave vector and $\mathbf{E}$- and H-field vectors) sum up to form an electromagnetic field described by a right-handed triplet of vectors k $(k_z<0)$, E, and H. It is in these regions that the negative propagation of light occurs. On the optical axis the orbital energy flow, proportional to the light intensity, is shown to be positive, while the spin flow is negative and exceeds the orbital flow in magnitude. That is why the on-axis summary energy flow is negative. The magnitude of the reverse flow on the optical axis is two times lower than that of the intensity. A similar mechanism may apply to the case of sharply focusing a laser beam with second-order polarization or phase singularity. Using two identical micro-objectives with a numerical aperture of 0.95, it has been demonstrated experimentally that the intensity on the optical axis near the focus of an optical vortex with a topological charge of 2 is zero for right circular polarization and nonzero for left circular polarization. This confirms that in the latter case there is the reverse flow of light energy on the optical axis, since in the center of the measured energy flow distribution there is a very weak local maximum (the Arago spot) aroused due to diffraction of the forward flow by a circle with a diameter of 300 nm (the diameter of the tube with the reverse flow). Comparing the numerical and experimental intensity distributions, it is possible to determine the diameter of a “tube” with the reverse flow. For a numerical aperture of 0.95 and a wavelength of 532 nm, the diameter of the tube of the reverse flow along the optical axis is 300 nm. It is also shown experimentally that when an optical beam with second-order cylindrical polarization is focused with a numerical aperture of 0.95, there is a circularly symmetric energy flow in the focus with a very weak flow in the center (the Arago spot), whose distribution is determined by diffraction of the forward flux by an $\sim 300$-nm-diameter circular area, where the energy flow is reverse. This also confirms that in the latter case, there is a reverse energy flow on the optical axis.

The matrix product state (MPS) belongs to the most important models in, for example, quantum information sciences and condensed-matter physics. However, realizing an $N$-qubit MPS with large $N$ and large entanglement on a quantum platform is extremely challenging, since it requires high-level qudits or $n$-qubit gates with $n\gg 2$ to carry or produce the entanglement. In this work, an efficient method that accurately encodes a given MPS into a quantum circuit with only one- and two-qubit gates is proposed. Essentially different from the existing compiling methods, our idea is to construct the unitary matrix product operators that optimally disentangle the MPS to a product state. These matrix product operators form the quantum circuit that evolves a product state to the targeted MPS with a high fidelity. Our benchmark on the ground-state MPSs of the strongly correlated spin models show that the constructed quantum circuits can simulate the MPSs with much fewer qubits than the sizes of the MPSs themselves. This method paves a feasible and efficient path to realizing useful and/or exotic quantum states and MPS-based models as quantum circuits on near-term quantum platforms.

We employ an ab initio theory to address several inconsistencies of the empirical scaling of photo-double-ionization (PDI) to electron impact ionization suggested by Samson [Phys. Rev. Lett. 65, 2861 (1990)]. We do so (i) by isolating the only relevant dipole component of the electron impact ionization and (ii) by replacing the static scaling of Samson, who used an effective cross-section area of the ion remainder, with dynamic scaling using the squared momentum of the photoelectron. The modified scaling is tested in the He $1s^2$ isoelectronic sequence and the combined inner shell $1s$ and valence shell $2p$ PDI of the negative ${\mathrm{F}}^{-}$ ion [Müller et al., Phys. Rev. Lett. 120, 133202 (2018)].

In the strongly interacting limit of the Hubbard model localized double occupancies form effective hard-core bosonic excitations, called doublons, which are long lived due to energy conservation. Using time-dependent density-matrix renormalization group methods we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analyzing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous emergence of an $\eta$ quasicondensate. Building on this, we study the effect of periodically driving the system during the expansion. Floquet analysis reveals that doublon hopping and doublon repulsion are strongly renormalized by the drive, breaking the $\eta \text{−}\mathrm{SU}\left(2\right)$ symmetry of the Hubbard model. Numerical simulation of the driven expansion dynamics demonstrates that the momentum in which doublons quasicondense can be controlled by the driving amplitude. These results point to new pathways for engineering nonequilibrium condensates in fermionic cold-atom experiments and are potentially relevant to driven solid-state systems.

We analyze several puzzling features of a recent experiment with a noninteracting gas of atoms in a quadrupole trap. After an initial momentum kick, the system reaches a stationary, quasithermal state even without collisions, due to the dephasing of individual particle trajectories. Surprisingly, the momentum distribution remains anisotropic at long times, characterized by different temperatures along the different directions. In particular, there is no transfer of the kick energy between the axial and radial trap directions. To understand these effects we discuss and solve two closely related models: a spherically symmetric trap $V\left(r\right)\simeq r^{\alpha }$ and a strongly confined gas along one direction (a pancake trap). We find that in the isotropic trap, the gas unexpectedly also preserves the anisotropy of the kick at long times, which we are able to explain using the conservation of angular momentum and the virial theorem. Depending on the value of $\alpha$ we find that the kick can cool or heat the orthogonal directions. The pancake trap case is quantitatively similar to the quadrupole one. We show that for the former, the temperature anisotropy and memory of the kick direction are due to the change in the two-dimensional effective potential resulting from the kick, thereby also explaining the quadrupole experimental results.

We develop a scaling law for a class of statistically nonstationary scalar optical fields, which ensures spectral invariance on their propagation into the far zone of a planar source. The invariance involves the constraint that the normalized far-zone spectrum must be the same in every direction of observation, as well as equal to the normalized area-averaged source spectrum. Thus, it additionally represents an extension of the earlier work by Wolf on stationary fields [Phys. Rev. Lett. 56, 1370 (1986)] that assumed the normalized source spectrum as independent of position. We present examples of both nonstationary and stationary fields that satisfy the scaling law and extended spectral invariance.

The NOON states are valuable quantum resources, which have a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Here we propose a fast, concise, and reliable protocol for deterministically generating the NOON states of two resonators coupled to a single $▵$-type superconducting qutrit. In particular, we derive the effective Hamiltonians at the points of the multiphoton resonances by virtue of the strong counter-rotating interaction between the resonator modes and the qutrit. Based on these crucial effective Hamiltonians, our protocol simplifies the previous ones using the single-photon resonance and consequently reduces the number of operations for state preparation. To test the robustness of this protocol, we analyze the effects from both the decoherence including dissipation and dephasing and the crosstalk of resonator modes on the state fidelity through a Lindblad master equation in the eigenbases of the full Hamiltonian.

We discuss an implementation of the minimum error state discrimination measurement, originally introduced by Helstrom [Quantum Detection and Estimation Theory (Academic Press, New York, 1976)]. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first entangled to an ancillary system and the measurement is performed on the ancilla. We show that, by an appropriate choice of the entanglement transformation, the Helstrom bound can be attained. The advantage of this approach is twofold. First, it provides an implementation when the optimal projective measurement cannot be directly performed. For example, in the case of continuous variable states (binary and $N$ phase-shifted coherent signals), the available detection methods, photon counting and homodyning, are insufficient to perform the required cat-state projection. In the case of symmetric states, the square-root measurement is optimal, but it is not easy to perform directly for more than two states. Our approach provides a feasible alternative in both cases. Second, the measurement is nondestructive from the point of view of the original system and one has a certain amount of freedom in designing the post-measurement state, which can then be processed further.

Solving linear differential equations (LDEs) is a hard problem for classical computers, while quantum algorithms have been proposed to be capable of speeding up the calculation. However, they are yet to be realized in experiment as it cannot be easily converted into an implementable quantum circuit. Here, we present and experimentally realize an implementable gate-based quantum algorithm for efficiently solving the LDE problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\mathbf{b}$, and an initial vector $\mathbf{x}\left(0\right)$, we obtain a target vector $\mathbf{x}\left(t\right)$ as a function of time $t$ according to the constraint $d\mathbf{x}\left(t\right)/dt=\mathcal{M}\mathbf{x}\left(t\right)+\mathbf{b}$. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances, and a gate-based quantum circuit is produced which is friendly to the experimentalists and implementable in current quantum techniques. In addition, we experimentally solve a $4\times 4$ linear differential equation using our quantum algorithm in a four-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one-dimensional quantum walk partially reflects information, as observed by absorption probability computations. In this paper, we shift our sights from the local phenomena of absorption probabilities to the global behavior of finite absorbing quantum walks in one dimension. We conduct our analysis by approximating the eigenbasis of the associated absorbing quantum walk operator matrix $Q_n$, where $n$ is the lattice size. The conditional probability distributions of these finite absorbing quantum walks exhibit distinct behavior at various timescales, namely wavelike reflections for times $t=O\left(n\right)$, fractional quantum revivals for $t=O\left(n^2\right)$, and stability for $t=O\left(n^3\right)$. At the end of this paper, we demonstrate the existence of fractional quantum revivals in other sufficiently regular quantum walk systems.

We investigate the parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetry violating effects in the CdH molecule and perform the relativistic coupled-cluster calculation of the molecular parameters—$E_{\text{eff}}, W_{\text{s}}$, and $W_{\text{M}}$—related to the electric dipole moment of electron (eEDM) interaction, the scalar-pseudoscalar (S-PS) nucleus-electron neutral current coupling, and the nuclear magnetic quadrupole moment (MQM) interaction with electrons, respectively. We also compute the molecular dipole moment and the magnetic hyperfine structure coupling constant of CdH. The values of $E_{\text{eff}}, W_{\text{s}}$, and $W_{\text{M}}$ obtained by us in the said molecule are 12.2 GV/cm, 14.0 kHz, and $0.82\times {10}^{33}$ Hz/e ${\mathrm{cm}}^2$, respectively, within an uncertainty of 10%. Furthermore, we study the trend of electron-correlation in the computed properties of CdH and that of the $\mathcal{P},\mathcal{T}$-odd parameters in the group-12 monohydrides (i.e., ZnH, CdH, and HgH).

The dual-laser plasma method has been used to record photoabsorption spectra of Tm, $\mathrm{T}{\mathrm{m}}^{+}$, and $\mathrm{T}{\mathrm{m}}^{2+}$ ions. The dominant process is $4d$ photoexcitation, giving rise to structure in the 140–240-eV region while structure due to $5p$ excitation is observed in the 27–38-eV region. Due to successive removal of $6s$ electrons outside a $4f^{13}$ core with increasing ionization, the $4d$ photoabsorption spectra of Tm, $\mathrm{T}{\mathrm{m}}^{+}$, and $\mathrm{T}{\mathrm{m}}^{2+}$ are very similar. The spectrum of neutral thulium shows autoionizing resonances, excited from both fine-structure levels of the $4f^{13}6s^2$ ground state, evidenced by a clear double-peaked Fano structure in the 140–240-eV range. Similar features are observed and can be associated with $4d\text{−}4f$ transitions in $\mathrm{T}{\mathrm{m}}^{+}$ and $\mathrm{T}{\mathrm{m}}^{2+}$. Broad structure, distinctly different from the spectra of Tm, $\mathrm{T}{\mathrm{m}}^{+}$, and $\mathrm{T}{\mathrm{m}}^{2+}$, in the same $4d\text{−}4f$ region of the spectrum at 25 ns suggests that $\mathrm{T}{\mathrm{m}}^{3+}$, with a different number of $4f$ electrons, may be present in the absorbing plasma immediately after its formation. Significant broadening due to autoionization was observed in the $5p$ absorption region for all three ion stages. The observed transitions were identified with the aid of the cowan suite of codes, which are based on Hartree-Fock with configuration interaction approach.

We study the ground-state properties of a two-component fermionic mixture effectively confined in a one-dimensional harmonic trap. We consider scenarios when numbers of particles in components are the same but particles have different masses. We examine whether it is possible to detect signatures of an unconventional pairing between opposite-spin fermions in the presence of attractive interactions. For this purpose, we perform the exact diagonalization of the many-body Hamiltonian and study the two-particle reduced density matrix. In agreement with expectations, we confirm that the many-body ground state is dominated by conventional pairs with a negligible total momentum for a small mass imbalance. Furthermore, we show that for sufficiently large mass ratios the domination of fundamentally different pairs is established and the Fulde-Ferrell-Larkin-Ovchinnikov phase is supported. Finally, we argue that the two mechanisms can coexist in the regime of moderate mass ratios. Due to the current experimental progress in obtaining ultracold fermionic systems in a few-body regime, our predictions may have some importance for the upcoming experiments.

The behavior of a neutral particle with magnetic quadrupole moment that interacts with axial magnetic and electric fields is analyzed. From the interaction of the magnetic quadrupole moment with the axial magnetic field, a spectrum of energy analogous to a Coulomb potential in two dimensions is obtained. Furthermore, the presence of an axial electric field is also considered. From the interaction of the magnetic quadrupole moment with this electric field, an analog of the Aharonov-Bohm effect is obtained. Finally, the Aharonov-Bohm effect for bound states is analyzed when this neutral particle system is subject to the two-dimensional harmonic oscillator.

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by tracing out part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state is reduced given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. One of our main technical results is a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. We demonstrate the viability of this approach with two examples of limited-resolution observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the one-dimensional Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity.

Quantum machine learning explores the devising and implementing of quantum software to enable the speedup for a classical machine learning counterpart, which has attracted extensive attention. The quantum Boltzmann machine is a promising quantum machine learning model and can be executed on near-term quantum devices to demonstrate quantum supremacy. We investigate an efficient algorithm for training a quantum Boltzmann machine based on a continuous-time quantum cluster Monte Carlo method realized with a dimension-expanded equivalent Hamiltonian. The proposed algorithm is capable of efficiently training various types of quantum Boltzmann machines, including a two-dimensional random transverse Ising Hamiltonian and other stochastic $\kappa$-local $(\kappa \ge 2)$ Hamiltonians. We further apply a quantum mean-field method to speed up the training process through discarding the quantum fluctuations of visible-hidden interactions. The experiment results show that our algorithm-trained quantum Boltzmann machine is more efficient on a small and large data set in terms of network convergence and time complexity.